Error correcting codes, such as Reed-Solomon codes, have a wide range of applications in digital communications and storage. Reed-Solomon codes, for example, add redundant bits to a digital stream prior to transmission or storage, so that a decoder can detect and possibly correct errors caused by noise or other interference. Generally, a Reed-Solomon encoder takes a block of digital data, comprising a sequence of digital information bits, and interprets the data as a sequence of information symbols. Each symbol comprises m bits of the digital information sequence. The block of input data comprises r such information symbols. The Reed-Solomon encoder produces p additional redundant symbols, which are concatenated with the k information symbols to form a codeword comprising n (equal to r plus p) symbols.
Errors occur during transmission or storage for a number of reasons, such as noise, interference, or defects on a storage medium. A Reed-Solomon decoder processes each block and attempts to correct errors and recover the original data. The number and type of errors that can be corrected depends on the characteristics of the Reed-Solomon code. In general, an RS(n,r) decoder can correct any combination of up to T=p/2 corrupted symbols per codeword provided that the remainder of the n symbols of the codeword are correct.
A Viterbi detector is typically used in a read channel of a magnetic recording system to detect the read data bits in the presence of intersymbol interference and noise. Thereafter, a Reed-Solomon decoder is often applied to correct any errors in the detected data and recover the original data. Nonetheless, a number of errors often remain. Thus, a number of techniques have been proposed or suggested for performing error-erasure Reed-Solomon decoding when such hard Reed-Solomon decoding fails. Generally, an error-erasure Reed-Solomon decoder evaluates reliability information associated with the detected data and repeatedly performs error-erasure decoding using the hard decision bits provided by the Viterbi detector and an erasure list until there is no decoding error. Such reliability information may be obtained, for example, from a Soft-Output Viterbi Algorithm (SOVA).
While such proposed error-erasure decoding techniques improve the performance of Reed-Solomon decoders, they suffer from a number of limitations, which if overcome, could lead to better error rate performance achievable by magnetic recording systems. In addition, previous techniques for error-erasure decoding are too complex for a practical implementation. A need therefore exists for improved techniques for error-erasure decoding that improve the performance of magnetic recording systems with manageable hardware cost or computational effort. An error-erasure decoding system incorporating these improved techniques is referred to as iterative error-erasure decoding system.